This paper discusses on how the number of independent cointegrating relations known as the cointegrating rank can be formulated and detected when some finite lag order vector autoregressive (VAR) schemes are fitted without imposing the assumptions which make the Granger representation theorem (GRT) hold. Adopting a generalized framework on the data generation processes (DGPs) and theoretically formulating each of the VAR schemes as a linear least-square predictor, we show that it precisely captures the cointegrating rank even if the existence of the VAR representation in GRT is not ensured. It is also established that estimating the rank through direct application of one of the information criteria under any finite lag order VAR scheme leads to some asymptotic desirability such as the conventional consistency. For finite sample performances of the estimation procedure proposed, some Monte Carlo experiments are executed, and it is observed that those are not so far from the asymptotics established theoretically, although affected by the selection of the scheme fitted or its lag order. We also point out that under finite sample sizes, the schemes specified by comparatively small lags such as 1 to 3 tend to produce desirable estimation results.